I've actually struggled with how to properly simplify this rational function, and I'm hoping someone can point me in the right direction. It's part of my precalculus class/section on graphing rational functions by translation:
$f(x)=\frac{-x}{7x+5}$
I can get along OK with simpler such rational functions, but this one is throwing me for a loop, because of the (-x) in the numerator.
Any help is greatly appreciated! I'm sorry for any formatting problems in advance, as I'm new to this site.
Thank you!
Find an equivalent form which you can already graph by translations: $$f(x)=\frac{-x}{7x+5}=\ -\frac{x+5/7}{7x+5}\ +\frac{5/7}{7x+5}\ =\\ = -\frac17\ +\frac 5{49x+35}\,. $$